<h4>Tool</h4><table border="0"><tr><td valign="top"><b>Name</b></td><td valign="top">Accumulation Functions</td></tr><tr><td valign="top"><b>ID</b></td><td valign="top">18</td></tr><tr><td valign="top"><b>Author</b></td><td valign="top">Copyrights (c) 2009 by Volker Wichmann</td></tr><tr><td valign="top"><b>Specification</b></td><td valign="top">grid</td></tr></table><hr><h4>Description</h4>Provides "accumulation functions" that can be used to e.g. move material over a "local drain direction" (LDD) network. The LDD net is computed for the supplied surface by MFD and D8 flow-routing algorithms. It is possible to switch from MFD to D8 as soon as a threshold is exceeded.
The input to each cell on the grid can be supplied from e.g. time series and the material can be moved over the net in several ways. All of these, except the "accuflux" operation, compute both the flux and the state for a given cell. For time series modelling (batch processing), the state of each cell at time t can be initialized with the previous state t - 1.
The capacity, fraction, threshold and trigger operations compute the fluxes and cell states at time t + 1 according to cell-specific parameters that control the way the flux is computed. The capacity function limits the cell-to-cell flux by a (channel) capacity control; the fraction function transports only a given proportion of material from cell to cell, the threshold function transports material only once a given threshold has been exceeded, and the trigger function transports nothing until a trigger value has been exceeded (at which point all accumulated material in the state of the cell is discharged to its downstream neighbour(s)).

The following operations are supported:

	* ACCUFLUX: The accuflux function computes the new state of the attributes for the cell as the sum of the input cell values plus the cumulative sum of all upstream elements draining through the cell.

	* ACCUCAPACITYFLUX / STATE: The operation modifies the accumulation of flow over the network by a limiting transport capacity given in absolute values.

	* ACCUFRACTIONFLUX / STATE: The operation limits the flow over the network by a parameter which controls the proportion (0-1) of the material that can flow through each cell.

	* ACCUTHRESHOLDFLUX / STATE: The operation modifies the accummulation of flow over the network by limiting transport to values greater than a minimum threshold value per cell. No flow occurs if the threshold is not exceeded.

	* ACCUTRIGGERFLUX / STATE: The operation only allows transport (flux) to occur if a trigger value is exceeded, otherwise no transport occurs and storage accumulates.

References:
BURROUGH, P.A. (1998): Dynamic Modelling and Geocomputation.- In: LONGLEY, P.A., BROOKS, S.M., MCDONNELL, R. & B. MACMILLAN [Eds.]: Geocomputation: A Primer. John Wiley & Sons, pp. 165-191.
<hr><h4>Parameters</h4><table border="1" width="100%" valign="top" cellpadding="5" rules="all"><tr><th>Name</th><th>Type</th><th>Identifier</th><th>Description</th><th>Constraints</th></tr>
<tr><th colspan="5">Input</th></tr><tr><td>Surface </td><td>Grid (input)</td><td>SURFACE</td><td>Surface used to derive the LDD network, e.g. a DTM.</td><td></td></tr><tr><td>Input </td><td>Grid (input)</td><td>INPUT</td><td>Grid with the input values to accumulate.</td><td></td></tr><tr><td>State t (*)</td><td>Grid (optional input)</td><td>STATE_IN</td><td>Grid describing the state of each cell at timestep t.</td><td></td></tr><tr><td>Operation Control (*)</td><td>Grid (optional input)</td><td>CONTROL</td><td>Depending on mode of operation either transport capacity, transport fraction, threshold value or trigger value.</td><td></td></tr><tr><td>Linear Flow Control Grid (*)</td><td>Grid (optional input)</td><td>CTRL_LINEAR</td><td>The values of this grid are checked against the linear flow threshold to decide on the flow-routing algorithm.</td><td></td></tr><tr><th colspan="5">Output</th></tr><tr><td>Flux</td><td>Grid (output)</td><td>FLUX</td><td>Flux out of each cell, i.e. everything accumulated so far.</td><td></td></tr><tr><td>State t + 1 (*)</td><td>Grid (optional output)</td><td>STATE_OUT</td><td>Grid describing the state of each cell at timestep t + 1.</td><td></td></tr><tr><th colspan="5">Options</th></tr><tr><td>Operation</td><td>Choice</td><td>OPERATION</td><td>Select a mode of operation</td><td>Available Choices:
[0] accuflux
[1] accucapacityflux / state
[2] accufractionflux / state
[3] accuthresholdflux / state
[4] accutriggerflux / state
Default: 0</td></tr><tr><td>Switch to Linear Flow</td><td>Boolean</td><td>LINEAR</td><td>Switch from MFD8 to D8 if linear flow threshold is crossed.</td><td>Default: 1</td></tr><tr><td>Threshold Linear Flow</td><td>Floating point</td><td>THRES_LINEAR</td><td>Threshold for linear flow, if exceeded D8 is used.</td><td>Default: 0.000000</td></tr></table>(*) <i>optional</i>